Boris M Smirnov Plasma Processes and Plasma Kinetics 586 Worked Out Problems for Science and Technology This Page Intentionally Left Blank Boris M Smirnov Plasma Processes and Plasma Kinetics 1807–2007 Knowledge for Generations Each generation has its unique needs and aspirations When Charles Wiley first opened his small printing shop in lower Manhattan in 1807, it was a generation of boundless potential searching for an identity And we were there, helping to define a new American literary tradition Over half a century later, in the midst of the Second Industrial Revolution, it was a generation focused on building the future Once again, we were there, supplying the critical scientific, technical, and engineering knowledge that helped frame the world Throughout the 20th Century, and into the new millennium, nations began to reach out beyond their own borders and a new international community was born Wiley was there, expanding its operations around the world to enable a global exchange of ideas, opinions, and know-how For 200 years, Wiley has been an integral part of each generation’s journey, enabling the flow of information and understanding necessary to meet their needs and fulfill their aspirations Today, bold new technologies are changing the way we live and learn Wiley will be there, providing you the must-have knowledge you need to imagine new worlds, new possibilities, and new opportunities Generations come and go, but you can always count on Wiley to provide you the knowledge you need, when and where you need it! William J Pesce President and Chief Executive Officer Peter Booth Wiley Chairman of the Board Boris M Smirnov Plasma Processes and Plasma Kinetics 586 Worked Out Problems for Science and Technology The Author Prof Boris M Smirnov Institute for High Temperatures Russian Academy of Sciences Moscow, Russia bsmirnov@orc.ru All books published by Wiley-VCH are carefully produced Nevertheless, authors, editors, and publisher not warrant the information contained in these books, including this book, to be free of errors Readers are adviced to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate Library of Congress Card No: applied for British Library Cataloging-in-Publication Data A catalogue record for this book is available from the British Library Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available in the Internet at http://dnb.d-nb.de © 2007 WILEY-VCH Verlag GmbH & Co KGaA, Weinheim All rights reserved (including those of translation into other languages) No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into machine language without written permission from the publishers Registered names, trademarks, etc used in this book, even when not specifically marked as such, are not to be considered unprotected by law Typesetting Hilmar Schlegel, Berlin Printing betz-druck GmbH, Darmstadt Bookbinding Litges & Dopf Buchbinderei GmbH, Heppenheim Printed in the Federal Republic of Germany Printed on acid-free paper ISBN: 978-3-527-40681-4 Druckfreigabe/approval for printing Without corrections/ ohne Korrekturen ❏ After corrections/ nach Ausführung der Korrekturen ❏ Date/Datum: Signature/Zeichen: V Contents Preface IX 1.1 1.2 1.3 1.4 1.5 1.6 Distributions and Equilibria for Particle Ensembles Distributions of Identical Atomic Particles Statistics of Bose–Einstein and Fermi–Dirac Distribution of Particle Density in External Fields 13 Laws of Black Body Radiation 18 Ionization and Dissociation Equilibrium 21 Ionization Equilibrium for Clusters 25 2.1 2.2 2.3 2.4 2.5 Elementary Processes in Plasma 33 Elementary Act of Particle Collision 33 Elastic Collision of Two Particles 37 Elastic Scattering of Classical Particles 39 Phase Theory of Particle Elastic Scattering 51 Total Cross Section of Elastic Collision 59 3.1 3.2 3.3 3.4 3.5 Slow Atomic Collisions 63 Slow Collisions of Heavy Atomic Particles 63 Resonant Charge Exchange and Similar Processes 74 Processes Involving Negative Ions 85 Three-Body Processes 91 Principle of Detailed Balance 95 4.1 4.2 4.3 4.4 Collisions Involving Electrons 99 Inelastic Electron–Atom Collisions 99 Atom Quenching by Electron Impact 103 Atom Ionization by Electron Impact 107 Recombination of Electrons and Ions 117 Plasma Processes and Plasma Kinetics Boris M Smirnov Copyright © 2007 WILEY-VCH Verlag GmbH & Co KGaA, Weinheim ISBN: 978-3-527-40681-4 VI Contents 5.1 5.2 5.3 5.4 Elementary Radiative Processes in Excited Gases 127 Broadening of Spectral Lines 127 Cross Sections of Radiative Tansitions 140 Absorption Coefficient for Resonant Photons 144 Absorption Coefficient in Molecular Gases 147 6.1 6.2 6.3 6.4 6.5 Boltzmann Kinetic Equation 153 Boltzmann Equation for a Gas 153 Peculiarities of Statistical Description of Gas Evolution 155 Integral Relations from the Boltzmann Equation 161 Stepwise Quantities and Processes 173 Collision Integral for Electrons 181 7.1 7.2 7.3 7.4 7.5 Transport and Kinetics of Electrons in Gases in External Fields 189 Electron Drift in a Gas in an Electric Field 189 Energy Balance for Electrons Moving in a Gas in an Electric Field 198 Dynamics of Electrons in a Gas in Electric and in Magnetic Fields 202 Conductivity of a Weakly Ionized Gas 212 Thermal Conductivity and Thermal Diffusion of Electrons in a Gas 217 8.1 8.2 8.3 8.4 8.5 8.6 Transport of Ions and Atoms in Gases and Plasmas 223 General Peculiarities of Transport Processes 223 Thermal Conductivity and Viscosity of Atomic Gases 229 Diffusion and Drift Character of Particle Motion 234 Chapman–Enskog Approximation 239 Diffusion of Ions in Gas in an External Electric Field 245 Transport of Atomic Ions in the Parent Gas in an External Electric Field 255 9.1 9.2 9.3 9.4 9.5 Kinetics and Radiative Transport of Excitations in Gases 265 Resonant Radiation of Optically Thick Layer of Excited Gas 265 Radiation Transport in Optically Thick Medium 273 Emission of Infrared Radiation from Molecular Layer 275 Propagation of Resonant Radiation in Optically Thick Gas 288 Kinetics of Atom Excitation by Electron Impact in a Gas in Electric Field 293 10 10.1 10.2 10.3 10.4 10.5 Processes in Photoresonant Plasma 303 Interaction of Resonant Radiation and Gas 303 Excited Atoms in Photoresonant Plasma 308 Processes in Photoresonant Plasma Involving Electrons 312 Propagation of Excitation and Ionization Waves 326 Heating of Atoms and Expanding of Photoresonant Plasma 329 Contents 11 11.1 11.2 11.3 11.4 11.5 11.6 11.7 Waves in Plasma and Electron Beams 335 Oscillations in an Isotropic Weakly Ionized Gas 335 Plasma Oscillations in Magnetic Field 346 Propagation of Electromagnetic Waves in Plasma 348 Electromagnetic Waves in Plasma in Magnetic Field 353 Damping of Waves in Plasma 357 Dynamics of Electron Beams in Plasma 365 Beam-Plasma Instabilities 371 12 12.1 12.2 12.3 12.4 12.5 Relaxation Processes and Processes with Strong Interaction in Plasma 377 Relaxation Processes in Plasma 377 Thermal Phenomena and Thermal Waves in Plasma 382 Plasma in Magnetic Field 393 Nonlinear Phenomena in Plasma 402 Plasma Structures 414 13 13.1 13.2 13.3 13.4 Cluster Plasma 421 Equilibrium of Clusters in Vapor 421 Kinetics of Cluster Growth in Plasma 425 Charging of Clusters 440 Cluster Transport 447 14 14.1 14.2 14.3 14.4 14.5 14.6 Aeronomy Processes 457 Oxygen Atoms in the Upper Atmosphere 457 Ions in the Upper Earth Atmosphere 464 Processes in the Earth Magnetosphere 471 Electromagnetic Waves in the Upper Atmosphere 476 Electric Phenomena in the Earth Atmosphere 480 Radiation of the Solar Photosphere 483 15 15.1 15.2 15.3 15.4 15.5 Gas Discharge Plasmas 487 Conditions of Self-Sustaining Gas Discharge 487 Cathode Region of Gas Discharge 496 Positive Column of Glowing Discharge of High Pressure 498 Heat Processes in Positive Column of High Pressure Discharge 514 Plasma of Positive Column of Low Pressure Discharge 520 16 16.1 16.2 16.3 16.3.1 16.3.2 Appendices 531 Appendix 1: Physical Constants 532 Appendix 2: Conversation Factors for Some Units 532 Appendix 3: Relations of Physics and Plasma Physics 533 Appendix 3a: Relations of General Physics 533 Appendix 3b: Relations for Physics of Gases and Plasmas 534 VII 558 16 Appendices 16.5.9 Positive Ions of Diatomics 16.5 Appendix 5: Atomic Parameters in the Form of Periodical Tables 559 560 16 Appendices 16.5.10 Negative Ions of Diatomics 16.5 Appendix 5: Atomic Parameters in the Form of Periodical Tables 561 This Page Intentionally Left Blank Druckfreigabe/approval for printing Without corrections/ ohne Korrekturen ❏ After corrections/ nach Ausführung der Korrekturen ❏ Date/Datum: Signature/Zeichen: 563 References A F Alexandrov, L S Bogdankevich, and A A Rukhadze Principles of Plasma Electrodynamics Berlin, Springer, 1984 J A Bittencourt Fundamentals of Plasma Physics Oxford, Pergamon Press, 1982 H V Boening Plasma Science and Technology Itaca, Cornell University Press, 1982 M I Boulos, P Fauchais, and E Pfender Thermal Plasmas New York, Plenum Press, 1994 S C Brown Basic Data of Plasma Physics: The Fundamental Data on Electrical Discharges in Gases New York, Wiley, 1966 R A Cairns Plasma Physics Glasgow, Blackie, 1985 B Chapman Glow Discharge Processes New York, Wiley, 1980 F F Chen Introduction to Plasma Physics and Controlled Fusion New York, Plenum Press, 1984 J D Cobine Gaseous Conductors Dover, New York, 1958 10 W Ebeling, A Förster, V E Fortov, V K Gryasnov, and A Yu Polishchuk Thermophysical Properties of Hot Dense Plasmas Stuttgart, Teubner, 1991 11 G Ecker Theory of Fully Ionized Plasmas New York, Academic Press, 1972 12 W Elenbaas High Pressure Mercury Vapor Lamps and Their Applications Eindhoven, Philips Tech Lib., 1965 13 V E Fortov and I T Iakubov Physics of Nonideal Plasma New York, Hemisphere, 1990 14 D A Frank-Kamenetskii Plasma–The Fourth State of Matter New York, Plenum, 1972 15 V E Golant, A P Zhilinsky, and I E Sakharov Fundamentals of Plasma Physics New York, Wiley, 1980 16 J de Groot and J van Vliet The High Pressure Sodium Lamp Deventer, Philips Tech Lib., 1986 17 M F Hoyaux Arc Physics New York, Springer, 1968 18 J R Hollahan and A T Bell Techniques and Applications of Plasma Chemistry New York, Wiley, 1974 19 L G H Huxley and R W Crompton The Diffusion and Drift of Electrons in Gases Wiley, New York, 1974 Plasma Processes and Plasma Kinetics Boris M Smirnov Copyright © 2007 WILEY-VCH Verlag GmbH & Co KGaA, Weinheim ISBN: 978-3-527-40681-4 564 References 20 S Ishimary Plasma Physics: Introduction to Statistical Physics of Charged Particles Benjamin, Menlo Park, 1985 21 S Ishimary Statistical Plasma Physics Redwood City, CA, Addison-Wesley vol Basic Principles, 1992 vol Condensed Plasmas, 1994 22 M A Kettani and M F Hoyaux Plasma Engineering Wiley, New York, 1973 23 Yu D Korolev and G A Mesyats Physics of Pulsed Breakdown in Gases Ekaterinburg, URO Press, 1998 24 A N Lagarkov and I M Rutkevich Ionization Waves in Electrical Breakdown in Gases New York, Springer, 1994 25 M A Lieberman and A J Lichtenberger Principles of Plasma Discharge and Materials Processing New York, Wiley, 1994 26 E M Lifshits and L P Pitaevskii Physical Kinetics Oxford, Pergamon Press, 1981 27 V S Lisitsa Atoms in Plasmas Berlin, Springer, 1994 28 F Llewelyn-Jones The Glow Discharge New York, Methuen, 1966 29 W Lochte-Holtgreven Plasma Diagnostics New York, Am Inst Phys., 1995 30 L B Loeb Basic Processes of Gaseous Electronics Berkeley, University of California Press, 1955 31 E A Mason and E W McDaniel Transport Properties of Ions in Gases New York, Wiley, 1988 32 H S W Massey and E H S Burhop Electronic and Ionic Impact Phenomena Oxford, Oxford University Press, 1969 33 H S W Massey Negative Ions Cambridge, Cambridge University Press, 1976 34 H S W Massey Atomic and Molecular Collisions New York, Taylor and Francis, 1979 35 E W McDaniel and E A Mason The Mobility and Diffusion of Ions in Gases New York, Wiley, 1973 36 E W McDaniel, J B A Mitchell, and M E Rudd Atomic Collisions New York, Wiley, 1993 37 G A Mesyats and D I Proskurovsky Pulsed Electrical Discharges in Vacuum Berlin, Springer, 1989 38 E Nasser Fundamentals of Gaseous Ionization and Plasma Electronics New York, Wiley, 1971 39 W Neuman The Mechanism of the Thermoemitting Arc Cathode Berlin, Academic-Verlag, 1987 40 Y P Raizer Gas Discharge Physics Springer, Berlin, 1991 41 Y P Raizer, M N Schneider, and N A Yatzenko Radio-Frequency Capacitive Discharges Boca Raton, CRC Press, 1995 42 V P Schevel’ko and L A Vainstein Atomic Physics for Hot Plasmas Bristol, Institute of Physics, 1993 43 P P J M Schram Kinetic Theory of Gases and Plasmas Dordrecht, Kluwer, 1991 44 S R Seshardi Fundamentals of Plasma Physics New York, American Elsevier, 1973 References 45 A G Sitenko Fluctuations and Nonlinear Wave Interactions in Plasmas Oxford, Pergamon Press, 1982 46 A Sitenko and V Malnev Plasma Physics Theory London, Chapman and Hall, 1995 47 B M Smirnov Physics of Weakly Ionized Gases Moscow, Mir, 1981 48 B M Smirnov Negative Ions New York, McGraw-Hill, 1982 49 B M Smirnov Physics of Ionized Gases New York, Wiley, 2001 50 L Spitzer Physics of Fully Ionized Gases New York, Wiley, 1962 51 T H Stix Waves in Plasmas New York, American Institute of Physics, 1992 52 P A Sturrock Plasma Physics Cambridge, Cambridge University Press, 1994 53 O Toshoro Radiation Phenomena in Plasmas Singapore, World Scientific, 1994 54 A von Engel Electric Plasmas: Their Nature and Uses London, Taylor and Francis, 1983 55 J F Waymouth Electric Discharge Lamps Cambridge, MIT Press, 1971 56 Applied Atomic Collision Physics vol Atmospheric Physics and Chemistry, eds H S W Massey and D R Bates Academic Press, New York, 1982 57 Basis Plasma Physics eds A A Galeev and R N Sudan Amsterdam, North Holland, 1983 58 Electrical Breakdown in Gases, ed J A Rees, New York and Toronto, 1973 59 Electrical Breakdown in Gases, eds J M Meek and J D Craggs Chichester, Wiley, 1978 60 Plasma Science: From Fundamental Research to Technological Applications Washington, National Academy Press, 1995 61 Transport and Optical Properties of Nonideal Plasma eds G A Kobzev, I T Iakubov, and M M Popovich New York, Plenum Press, 1995 62 Vacuum Arcs ed J M Lafferty New York, Wiley, 1980 565 This Page Intentionally Left Blank Druckfreigabe/approval for printing Without corrections/ ohne Korrekturen ❏ After corrections/ nach Ausführung der Korrekturen ❏ Date/Datum: Signature/Zeichen: 567 Subject Index a Abnormal glow discharge 497 f Abnormal skin effect 352 Absorption coefficient 144 Absorption cross section 142 f Absorption function 148, 275 Acoustic oscillations 332 f Activation energy 384 Active centers 28 Adiabatic exponent 336 Adiabatic set of equations 65 Alfv´en speed 346 Alfv´en wave 346 Ambipolar diffusion 17, 470, 499 Amplitude of scattering 38 Arc discharge 517 f., 521 Associative ionization 312 Atmospheric ions 464 Atomic oxygen in atmosphere 458, 463 Attenuation factor 357, 360 Aurora 474 Autodetaching state 90 Autoionization state 120 b Balance equation 34 Barometric distribution 13 Beam-plasma instability 371 Bethe approximation 102 Biberman–Holstein equation 290 Black body radiation 18 Blanck law 252 Boltzmann distribution 1, 11 Boltzmann kinetic equation 154 Boltzmann statistics Born approximation 39, 53, 101 Bose-Einstein distribution Breakdown potential 493 Breit–Wigner formula 122 Broadening of spectral lines 127 Bunching of electrons 420 Buneman instability 376 Bursian current 369 c Capture cross section 43 Cathode drop 497 Cathode region 493 Cathode voltage 497 Chapman–Enskog approximation 239 Charge exchange process 30, 65 Charge separation 493 Charging of clusters 440 Charging of the Earth 480 Chemical potential ff Cluster charge 441 Cluster collision integral 188 Cluster diffusion 447 Cluster evaporation 96, 187, 421 Cluster growth 421, 433 Cluster instability 453 Cluster mobility 449 Cluster plasma 421 Cluster recombination 452 Cluster temperature 439 Coagulation 435, 438 Plasma Processes and Plasma Kinetics Boris M Smirnov Copyright © 2007 WILEY-VCH Verlag GmbH & Co KGaA, Weinheim ISBN: 978-3-527-40681-4 568 Subject Index Coalescence 435 Coefficient of ambipolar diffusion 17, 401, 500, 510 f., 520 Collapse of wave functions 159 Collision integral 153 Conductivity 212 Conductivity tensor 212 Continuity equation 162 Contraction of discharge 515 Conversion of atomic ions into molecular ions 94 Correlation function 129 Coulomb logarithm 51, 185, 202 Coupling constant of plasma 380 Critical cluster size 422 Critical electron temperature 316 Cross-fluxes 219 Current-convective instability 402 Current-voltage characteristic 498 Cyclotron frequency 216, 356 Cyclotron resonance 216 Cyclotron wave 355 d Damping of plasma oscillations 357 Dark discharge 487 Debye–Hückel radius 15, 345 Degenerate electron gas 11 Degree of supersaturation 187, 421 Delta-function model 85 Depolarization rate constant 307 Dielectric constant tensor 215 Dielectric particle 28 Dielectronic recombination 120 f Differential cross section 34, 39, 100, 155, 231 Diffusion coefficient 13, 163, 206, 224, 227, 246 Diffusion cross section 13 Diffusion motion of particles 235 Diffusion regime of cluster equilibrium 425 Dimensionality consideration 20, 94, 109 Dipole–dipole interaction 78 Dispersion relation 336, 353 Dissociating gas 234 Dissociative attachment 121 Dissociative equilibrium 24 Dissociative recombination 121, 464 Distance of closest approach 39, 69 Distribution function Distribution function on optical thicknesses 284 D-layer 469 Doppler broadening of spectral lines 128 Double layer 503 Drift velocity 167 Drift wave 348, 364, 410 e Earth magnetosphere 471 f Effective width of band 280, 286, 288 Efficiency of atom excitation 294 Einstein coefficient 142 Einstein relation 14 Einstein–Podolsky–Rosen pair 160 E-layer 466 Electric domain 411, 416 Electron attachment 28 Electron beam 365 Electron drift velocity 190, 198 Electron temperature 181, 196 Electron term 63 Electrophoresis 415, 511 Elenbaas–Heller equation 514 Elsasser function 150 Emission cross section 143 Energetic Townsend coefficient 488 Entangled processes 159 Entropy 157 ff Equilibrium plasma 112, 378 Euler equation 162 Exchange excitation 80 Subject Index Exchange interaction potential 66, 75 Exchange scattering 102 Excitation cross section 100, 102, 107 Excitation exchange 80 Excitation rate 187, 298 Excitation temperature 304, 323 Excitation transfer 80 f Faraday effect 353 Fermi potential 57 Fermi–Dirac distribution 10 Fine structure state transitions 81 First Townsend coefficient 488 F-layer 467 Fokker–Planck equation 176 Free fall velocity 451 Frequency distribution function 127 Frozen magnetic lines of force 346, 395 f Fuks formula 440 g Gas-discharge plasma 118, 342 Gaseousness criterion 36 Gas-kinetic cross section 143, 159, 358, 432, 450, 460, 473, 478 Gauss distribution 18, 174 Gibbs principle Glory point 61 Glow discharge 28, 496 ff Green function 290 Group velocity of waves 402 Growth of metal clusters 425 h Hall constant 212 Hall effect 204 Hard-sphere model 42, 159, 242 Hardening 381 heat capacity 165 Heat equation 162 Heat flux 163 Helicon wave 357 High conductivity plasma 394 Holtzmark function 138 H-theorem 157 Hybrid waves 355 i Ideal plasma 15 Ideality parameter 380 Ignition of discharge 488, 493 Impact broadening of spectral lines 133, 137 Impact parameter 34, 39, 49, 55, 74, 159, 185, 202, 255, 443 Intensity of radiative transition 148 Intersection of electron terms 65, 87, 89 Inverted population of levels 144 Ion attachment 28 Ion mobility 13 f., 213, 228, 239, 242, 252, 256 Ion sound 341 f., 358, 405 Ion-molecular processes 457, 466 Ionization cross section 108 Ionization equilibrium 21, 25 Ionization instability 398, 400 Ionosphere 351, 466, 470 k Kinematic viscosity 165 Kinetic coefficients 163, 223 Kinetic equation 153, 189 Kinetic regime of cluster equilibrium 425 Knudsen number 450 Korteweg–de Vries equation 403 l Landau collision integral 183 Landau damping factor 358 Landau–Zener case 69 Langevin formula 441 Langmuir frequency 338 Langmuir paradox 374 Langmuir soliton 409 569 570 Subject Index Larmor frequency 204 Laser operation 144 Lighthill criterion 402 Liquid drop model 51, 96 Local ionization equilibrium 382 Local thermodynamic equilibrium 454 Long-range interaction 64 Longitudinal diffusion coefficient 263 Longitudinal temperature 249 Longitudinal wave 341 Lorenz profile of spectral lines 128, 132 m Macroscopic equations 166 Magnetic field of Earth 471, 476 Magnetic field pressure 396 Magnetic lines of force 211, 346 Magnetic moment 208 Magnetic moment of Earth 471 Magnetic pressure 346, 396, 472, 534 Magnetic sound 346 Magnetic trap 212 Magnetohydrodynamic equations 393 Magnetohydrodynamic waves 346 Magnetosphere of Earth 356, 471 Maxwell distribution 5, 178 Maxwell equations 348 Mean free path 36 Mean free path of photons 309 Metal clusters 25 Metal-containing molecules 428 Mobility of charged particles 13 Mobility of neutral particles 13 Model of single spectral lines 283 Modulation instability 403 Momentum transport equation 162 Multicharge ions 120 Mutual neutralization of ions 87, 97 n Navier–Stokes equation 164 Nighttime atmosphere 465 Nonlinear ion sound 405 Nonlinear processes 402 Normal distribution 174 Normal glow discharge 497 Normal skin effect 351 Nucleation from metal vapor 425 Nucleation from metal-containing molecules 428 o Ohm’s law 212 Optical thickness 265, 267 Ozone decomposition wave 391 Ozone in atmosphere 461 p Parametric instability 411 Paschen law 493 P-branch of molecular transitions 150 Penning process 507 Phase space Phase theory of scattering 52 Phase velocity 341 Photodissociation 457 Photoionization 457 Photon flux 266 Photoresonant plasma 303 Pinch effect 397 Pinch instability 398 Planck distribution 19 Planck radiation formula 19 Plasma fluctuations 375 Plasma frequency 338 Plasma instabilities 363 Plasma oscillations 338, 341 Plasma relaxation 377 Plasma waves 358 Poincare instability 158 Poisson formula 175 Polarizability 44, 93 Subject Index Polarization capture cross section 45, 62 Polarization diffusion cross section 49, 93 Positive column of discharge 496 Pressure of gas 162 Pressure tensor 162, 228 Principle of detailed balance 118 Propagation of resonant radiation 326 Resonance photon 266, 303, 308 Resonant charge exchange 65 Resonant radiation 265, 288 Reynolds number 451 Richardson constant 24 Richardson–Dushman formula 23 Rosen–Zener case 71 Rosen–Zener–Demkov formula 73 Rotational distribution Runaway of electrons 201 q Quasimolecule 63 Quasineutrality of plasma 31 Quasistatic broadening of spectral lines 134 Quenching cross section 104 s Saha distribution 21 Scattering amplitude 38, 100 Scattering angle 34 Scattering length 58 Scattering phase 52 Schottky regime 500, 511 Schrödinger equation 37, 63 Schumann–Runge continuum 457 Second Townsend coefficient 488, 496 Self-consistent field 521 Self-maintained discharge 489 Self-reversal of spectral lines 268 Sena effect 255 Size distribution function of clusters 421 Skin effect 351 Slow collisions 63 Smoluchowski equation 176 Smoluchowski formula 440 Solar radiation 457 Solar wind 474 Soliton 403 Sonin polynomials 239 Sound generation 329 Sound velocity 336 Spectral radiation density 19 Spitzer formula 214 Spontaneous radiation 142 State equation 172 Statistical weight 3, Stephan–Boltzmann constant 20 Stephan–Boltzmann law 20 r Radiation belts of Earth 212, 474 Radiation flux 266 Radiative heat transfer 274 Radiative transitions 146 Ramsauer effect 58 Random model of spectral lines 275 Rate constant 28 Rate constant of atom ionization 194 Rayleigh–Jeans formula 19 R-branch of molecular transitions 150 Recombination coefficient 87, 117 Recombination of clusters 452 Recombination of electrons and ions 117 Recombination of positive and negative ions 87, 253 Reemission of photons 288 Regimes of electron equilibrium in plasma 192 Regular model the spectral lines 149 Relaxation processes 377 Relaxation time 230 571 572 Subject Index Stepwise ionization 118 Stimulated radiation 142 Stokes formula 449 Striations 417 Sun photosphere 483 Supersaturation degree 187, 421 Townsend coefficients 489 Transport coefficients 163, 223 Transversal temperature 249 Tsendin model 417 Tunnel electron transition 29 Two-state approximation 63 t Tau-approximation 154 Temperature 3, 162 Thermal conductivity coefficient 163, 229 Thermal diffusivity coefficient 165 Thermal instability 383 Thermal wave 382 Thermodiffusion coefficient 219 Thermodynamic equilibrium 14, 119 Thermoemission 23 Thomson model for atom ionization 107, 116 Thomson theory for three-body processes 93 Three-body processes 91 Three-body rate constant 92 Three-body recombination 93 Three-halves power law 366 Threshold ionization cross section 100, 113 Total cross section 53, 58 v Vibrational distribution Vibrational-relaxation wave 388 Vibrational-rotational molecular state Virial theorem 171 Viscosity coefficient 163, 225, 230, 234, 244 w Wave damping 357 Wave number 335 Wave packet 402 Weiskopf radius 60 Whistlers 355, 479 Width of autodetachment level 88, 120 Wien formula 19 Wigner–Seitz radius 51, 447 Work function 22 z Zeldovich formula 387 f ...Boris M Smirnov Plasma Processes and Plasma Kinetics 586 Worked Out Problems for Science and Technology This Page Intentionally Left Blank Boris M Smirnov Plasma Processes and Plasma Kinetics... Electron Beams in Plasma 365 Beam -Plasma Instabilities 371 12 12.1 12.2 12.3 12.4 12.5 Relaxation Processes and Processes with Strong Interaction in Plasma 377 Relaxation Processes in Plasma 377 Thermal... reabsorption processes The collective processes, oscillation plasma properties, and nonlinear plasma processes are represented in the corresponding problems Transport of particles in a plasma is